Generalisations of cubic xpreessions

Topic: cubics

Solving equations (and inequations)

Topics: equations, inequations

How to solve any quadratic equation

Topic: quadratic

Selecting the objects when order is NOT important

Topic: combination

Finding the equation of a line through a point and the point of intersection of two lines

Topic: cartesian geometry

looking at number patterns

Topic: series

The integration of the exponential function

Topics: exponential, integration

Integration that results in an inverse trig function

Topics: integration, inverse trig

Finding a more general way of finding the coefficients

Topic: binomial product

Using symmetry to sketch graphs

Topic: curve sketching

A different way of measuring angles

Topics: radians, trigonometry

Proving Pascal Triangle relationships using the binomial theorem

Topic: binomial theorem

Initial definitions & notations and the angle theorems

Topic: angle theorems

Using the first derivative to investigate the shape of curves

Topics: calculus, first derivative

The first of our angle theorems

Topics: circle geometry, angle theorems

How do we go back to the original curve?

Topic: calculus

The first of the tangent theorems

Topic: circle geometry

Finding a general solution for geometric series

Topics: series, sums

Using the theory to solve the problems

Topic: series

Introducing induction as applied to series type questions

Topic: induction

More on the Argand Diagram

Topic: complex numbers

If two quadratics are equal for more han two values, then they must be the same quadratic.

Topic: quadratic

Looking at the parametric representation of the parabola

Topics: parabola, parametric

Alternative ways of finding features

Topic: quadratics

Using the roots of one polynomial to create a new polynomial

Topic: polynomial

Lines & rays in the Argand diagram

Topics: complex numbers, locus

Factorising over rtge complex field

Topic: polynomials

How to find repeated roots

Topics: polynomials, multiple roots

Newton's Laws and how to use them in solving problems

Topics: motion, dynamics, acceleration

Integrating fractions involving polynomials

Topic: integration

Some past circle geo questions

Topic: circle geometry

Circular motion around a banked curve is very similar to the conical pendulum

Topics: banked curve, motion

All mathematical operations have an inverse that will "undo" the operation, including functions.

Topic: inverse functions

Defining the absolute value function

Topics: functions, absolute value

Working out how to move curves around

Topic: curve sketching

The parametric form of the hyperbola

Topics: parametric, hyperbola

Looking at what happens when the eccentricity is greater than 1.

Topics: conics, hyperbola

Curves can be described algebraically but also geometrically

Topic: locus

Using parameters to describe curves

Topic: parametric

Finding a generalisation for the chord of a parabola

Topics: parabola, parametric

The product rule for integration

Topics: integration, by parts

Using the derivative to measure the rate of change of physical quantities

Topics: calculus, rates of change

Shortest distance betrween a point and a line

Topic: distance

Putting all of the tools together to get a curve sketching menu.

Topics: calculus, curve sketching

A couple of different type of induction problems

Topic: induction

Classifying quadratics

Topic: quadratics

Definitions and initial theorems

Topics: geometry, angles

The classification of parabolas using the discriminant

Topics: quadratic, discriminant

differentiation via the method of first principles

Topics: calculus, first principles

Looking at both the algebraic and the geometrical way of describing curves.

Topic: locus

Deriving the t results for their use in trig questions

Topics: trigonometry, t results

Reducing equations to quadratics in order to solve.

Topic: quadratic

Some properties of the parabola.

Topic: parabola

Looking at the specific case of the locus as a parabola

Topics: parabola, locus

Eliminating the parameters in order to find the locus of points.

Topic: locus.parameters

Putting together all of the tools into a curve sketching menu.

Topics: calculus, curve sketching

Identifying key features of a curve

Topics: calculus, critical points, curve sketching

The reverse chain rule, an alternative way of approaching integrals that could otherwise been done by substitution.

Topic: integration

Solving trig equations

Topic: trigonometry

Deriving formulae for use with geometric aeries.

Topics: series, geometric

Introducing the geometric series

Topic: series

Investigating the area under curves more closely.

Topics: integration, areas

Results concerning polynomials

Topic: polynomials

The reaminder and factor theorems

Topics: polynomials, factor theorem, remainder theorem

When solving problems involving algebraic fractions, ALWAYS FACTORISE FIRST

Topics: algebra, algebraic fractions

Techniques for solving equations/imequations

Topics: equation, inequation

The idea behind solving quadratics

Topics: algebra, quadratic

General expressions for the factorising and expanding of cubics

Topics: algebra, cubic

Real numbers and som eof their characteristics

Topic: real numbesr

Defining real numbers, looking at divisibility tests and taking a closer look at fractions.

Topic: real numbers

Moving our basic curve around the plane

Topic: curve sketching

Tips for drawing polynomials

Topic: polynomials

Some tips for sketching polynomials.

Topics: polynomials, curve sketching

Further transformations of basic curves

Topic: curve sketching

Graphing inequalities on the number plane.

Topic: inequalities